I am performing survival analysis on credit data. I created a simple model with using interest rate:

`cox <- coxph(Surv(periods,charged_off) ~ int_rate, data=notes)`

I assumed that `int_rate`

was a time-independent variable, but the following test rejects H_{A}:

`> cox.zph(cox) rho chisq p int_rate 0.0446 14.2 0.000169 `

**Same result for other variables such as loan amount:**

`> cox <- coxph(Surv(periods,charged_off) ~ int_rate + loan_amnt, data=notes) > cox.zph(cox) rho chisq p int_rate 0.0364 9.31 2.28e-03 loan_amnt 0.0317 8.84 2.95e-03 GLOBAL NA 26.28 1.97e-06 `

**Plot for int_rate:**

Why would these covariates be considered time dependent? Am I doing something wrong? Thanks.

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#### Best Answer

The distinction one has to make is between time-varying covariate and a covariate whose coefficient changes over time. Both violate the proportionality assumption, but do not have to be drawbacks. Rather, they can and are often theoretically meaningful (see Singer & Willett's book on Longitudinal Data Analysis and their 1991 paper in Psychological Bulletin). They just have to be included in the model.

In your plot, it looks like the coefficient for that time-*invariant* predictor changes over time (becomes less strong) and therefore violates the proportionality assumption. Including an interaction with that covariate and time would solve things and get around the proportionality assumption. Again, Singer and Willett's book is a classic–and highly accessible. The companion website also has code and examples for software implementation.

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